Related papers: Specification of additional information for solvin…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…
We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
We consider an inverse problem in information diffusion modeled by random walks on combinatorial graphs. The problem concerns reconstruction of vertex centrality from the distribution of the first passage times observed on a subset of…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…